A Vector Autoregressive Moving Average Model for Interval-Valued Time Series Data

Abstract

Modelling and forecasting interval-valued time series (ITS) have received increasing attention in statistics and econometrics. An interval-valued observation contains more information than a point-valued observation in the same time period. The previous literature has mainly considered modelling and forecasting a univariate ITS. However, few works attempt to model a vector process of ITS. In this paper, we propose an interval-valued vector autoregressive moving average (IVARMA) model to capture the cross-dependence dynamics within an ITS vector system. A minimum-distance estimation method is developed to estimate the parameters of an IVARMA model, and consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. A two-stage minimum-distance estimator is shown to be asymptotically most efficient among the class of minimum-distance estimators. Simulation studies show that the two-stage estimator indeed outperforms other minimum-distance estimators for various data-generating processes considered.

Citation

Han, A., Hong, Y., Wang, S. and Yun, X. (2016), "A Vector Autoregressive Moving Average Model for Interval-Valued Time Series Data", Essays in Honor of Aman Ullah (Advances in Econometrics, Vol. 36), Emerald Group Publishing Limited, Leeds, pp. 417-460. https://doi.org/10.1108/S0731-905320160000036021